The federal paperwork filed in federal court detailed an alleged bribery scheme where Berea businessman Ferris Kleem paid for Las Vegas trips for both Dimora and Russo.
Neither Dimora nor Russo were named but the descriptions of Public Official One and Public Official Two match their job descriptions.
Neither has been charged and both have denied any wrongdoing.
Kleem allegedly arranged for Dimora to get the services of a Las Vegas call girl and Kleem brought the girl to Dimora's suite at the Mirage.
Dimora's lawyer Richard Lillie claims Dimora got a legal massage.
Dimora also allegedly got a refrigerator, a discount on a television, and payment for a Rolex watch from Kleem.
Rokakis made his remarks in an address to the Cleveland City Club Friday.
Earlier Friday he told Channel 3's Tom Beres, "Both Commissioner Dimora and Auditor Russo need to resign. People have danced around this issue for almost two years. The county is tired and weary of these allegations. There are indictments, people pleading guilty to bribing PO1 and PO2. This has gone on long enough we need to get on with the county's business."
Rokakis, Commissioners Tim Hagan and Peter Lawson Jones. and Governor Ted Strickland earlier asked for Dimora to step down.
Late Friday, Cuyahoga County Executive candidate Matt Dolan also called for Dimora and Russo to step down and praised Rokakis.
"I have privately (via a letter) and publicly demanded Jimmy Dimora and Frank Russo resign from their respective offices," Dolan said. "I am pleased to finally have a Cuyahoga County Democrat to join me in this pursuit."
"The actions of Dimora and Russo have crippled the county. Their resignations are one more step towards a return to an honest and efficient government."
Lillie says of Dimora,"He's not stepping down. He was elected to do a job and he will continue to do it."
Dimora's job will disappear at the end of the year as the county switches to a new form of government.